Zeitouni, Ofer
Overview
Works:  69 works in 203 publications in 2 languages and 2,123 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Other, Contributor, 956, 958, Editor 
Classifications:  QA273.67, 519.2 
Publication Timeline
.
Most widely held works by
Ofer Zeitouni
Large deviations techniques and applications by
Amir Dembo(
Book
)
40 editions published between 1992 and 2010 in English and held by 664 WorldCat member libraries worldwide
The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, biomolecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics. Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Zeitouni is a Professor of Mathematics at the Weizmann Institute of Science and at the University of Minnesota
40 editions published between 1992 and 2010 in English and held by 664 WorldCat member libraries worldwide
The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originally developed in the context of statistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantly different from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, biomolecular sequence analysis, hypothesis testing problems in statistics, and the Gibbs conditioning principle in statistical mechanics. Starting with the definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by their application. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations between the LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the sample paths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential equations from the domain of attraction of stable equilibria. They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Zeitouni is a Professor of Mathematics at the Weizmann Institute of Science and at the University of Minnesota
An introduction to random matrices by
Greg W Anderson(
Book
)
20 editions published between 2009 and 2011 in English and held by 309 WorldCat member libraries worldwide
The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently selfcontained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence
20 editions published between 2009 and 2011 in English and held by 309 WorldCat member libraries worldwide
The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently selfcontained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence
Lectures on probability theory and statistics : Ecole d'Eté de Probabilités de SaintFlour XXXII2002 by
Boris Tsirelson(
Book
)
22 editions published in 2004 in English and German and held by 97 WorldCat member libraries worldwide
This is yet another indispensable volume for all probabilists and collectors of the SaintFlour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in SaintFlour (July 724, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some twodimensional random curves. It provides a definition and properties of the SchrammLoewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar selfavoiding walks, critical percolation, looperased random walks and uniform spanning trees
22 editions published in 2004 in English and German and held by 97 WorldCat member libraries worldwide
This is yet another indispensable volume for all probabilists and collectors of the SaintFlour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in SaintFlour (July 724, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some twodimensional random curves. It provides a definition and properties of the SchrammLoewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar selfavoiding walks, critical percolation, looperased random walks and uniform spanning trees
Random media at SaintFlour by
F. den Hollander(
Book
)
7 editions published in 2012 in English and held by 13 WorldCat member libraries worldwide
7 editions published in 2012 in English and held by 13 WorldCat member libraries worldwide
A general classification rule for probability measures by
Ofer Zeitouni(
Book
)
5 editions published between 1991 and 1993 in English and held by 5 WorldCat member libraries worldwide
We consider the problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M1(sigma) over some compact Polish space E, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to a correct decision for any A satisfying certain structural assumptions. A refined decision procedure is also presented which, given a countable collection Ai C M1(sigma), i = 1, 2 ... each satisfying the structural assumption, will eventually determine a.s. the membership of the distribution in any finite number of the Ai. Applications to density estimation and the problem of order determination of Markov processes are discussed
5 editions published between 1991 and 1993 in English and held by 5 WorldCat member libraries worldwide
We consider the problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M1(sigma) over some compact Polish space E, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to a correct decision for any A satisfying certain structural assumptions. A refined decision procedure is also presented which, given a countable collection Ai C M1(sigma), i = 1, 2 ... each satisfying the structural assumption, will eventually determine a.s. the membership of the distribution in any finite number of the Ai. Applications to density estimation and the problem of order determination of Markov processes are discussed
Large deviations and applications : the finite dimensional case by
Amir Dembo(
Book
)
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
These notes, which form the first chapter of a forthcoming book, are intended to serve as lecture notes on the topic of large deviations and applications for students whose background and interests are in applications which involve finite dimensional spaces. Although narrow in their scope, these notes present a good deal of the methods available for more general situations. A glaring omission is the method of subadditivity, which will be discussed in another chapter in the book. Another deficiency of these notes is the sketchy bibliography and historical notes. We hope to correct this in the book
4 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
These notes, which form the first chapter of a forthcoming book, are intended to serve as lecture notes on the topic of large deviations and applications for students whose background and interests are in applications which involve finite dimensional spaces. Although narrow in their scope, these notes present a good deal of the methods available for more general situations. A glaring omission is the method of subadditivity, which will be discussed in another chapter in the book. Another deficiency of these notes is the sketchy bibliography and historical notes. We hope to correct this in the book
Can one decide the type of the mean from the empirical measure by
Sanjeev Kulkarni(
Book
)
4 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
The problem of deciding whether the mean of an unknown distribution is in a set Alpha or in its complement based on a sequence of independent random variables drawn according to this distribution is considered. Using large deviations techniques, an algorithm is proposed which is shown to lead to an a.s. correct decision for a class of Alpha which are necessarily countable. A refined decision procedure is also presented which, given a countable decomposition of Alpha, can determine a.s. to which set of the decomposition the mean belongs. This extends and simplifies a construction by Cover
4 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
The problem of deciding whether the mean of an unknown distribution is in a set Alpha or in its complement based on a sequence of independent random variables drawn according to this distribution is considered. Using large deviations techniques, an algorithm is proposed which is shown to lead to an a.s. correct decision for a class of Alpha which are necessarily countable. A refined decision procedure is also presented which, given a countable decomposition of Alpha, can determine a.s. to which set of the decomposition the mean belongs. This extends and simplifies a construction by Cover
Infinite dimensionality results for trajectory MAP estimation based on the Malliavin calculus by
Ofer Zeitouni(
Book
)
4 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1987 in English and held by 4 WorldCat member libraries worldwide
On the wavelet transform of fractional Brownian motion by J Ramanathan(
Book
)
3 editions published between 1989 and 1990 in English and held by 4 WorldCat member libraries worldwide
3 editions published between 1989 and 1990 in English and held by 4 WorldCat member libraries worldwide
Quenched, annealed and functional large deviations for onedimensional random walk in random environment by
Francis Comets(
Book
)
3 editions published in 1998 in English and Undetermined and held by 4 WorldCat member libraries worldwide
3 editions published in 1998 in English and Undetermined and held by 4 WorldCat member libraries worldwide
Some results on the problem of exit from a domain by
BenZion Bobrovsky(
Book
)
2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide
Recursive identification in continuoustime stochastic processes by
David Levanony(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Maximum aposteriori estimation of random fields by
Amir Dembo(
Book
)
2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1988 and 1989 in English and held by 3 WorldCat member libraries worldwide
Sanov's theorem for subsampling from individual sequences by
Amir Dembo(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Onsager Machlup functionals for a class of non trace class SPDE's by
Eddy MayerWolf(
Book
)
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
A nonstandard form of the rate function for the occupation measure of a Markov chain by Paul Dupuis(
Book
)
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
Robust diffusion approximation for nonlinear filtering by
R. Sh Lipt︠s︡er(
Book
)
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
On increasing subsequences of I.I.D. samples by
JeanDominique Deuschel(
Book
)
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
Quenched subexponential tail estimates for onedimensional random walk in random environment by
Nina Gantert(
Book
)
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
Maximum aposteriori estimation of random fields : elliptic Gaussian fields observed via a noisy channel by
Amir Dembo(
Book
)
2 editions published between 1988 and 1989 in English and held by 2 WorldCat member libraries worldwide
An extension of the "prior density for path" (OnsagerMachlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic Partial Differential Equations (PDEs) driven by white noise. This functional is then used to define and solve the MAP estimation of such fields observed via nonlinear noisy sensors. Existence results and a representation of the estimator are derived for this model
2 editions published between 1988 and 1989 in English and held by 2 WorldCat member libraries worldwide
An extension of the "prior density for path" (OnsagerMachlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic Partial Differential Equations (PDEs) driven by white noise. This functional is then used to define and solve the MAP estimation of such fields observed via nonlinear noisy sensors. Existence results and a representation of the estimator are derived for this model
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Related Identities
 Dembo, Amir Author
 Guionnet, Alice Other
 Anderson, Greg W. Author
 Tavaré, Simon Author
 Picard, Jean 1959 Editor
 SpringerLink (Service en ligne)
 SpringerLink (Online service)
 Center for Intelligent Control Systems (U.S.)
 Ṭekhniyon, Makhon ṭekhnologi leYiśraʼel Fakultah lehandasat hashmal
 Massachusetts Institute of Technology Laboratory for Information and Decision Systems
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Associated Subjects
Asymptotic expansions Calculus of variations Decomposition (Mathematics) Differential equations, Partial Distribution (Probability theory) Estimation theory Filters (Mathematics) Finance GeneticsMathematics HamiltonJacobi equations Large deviations Markov processes Mathematical physics Mathematical statistics Mathematics PolymersMathematical models Population geneticsMathematical models Population geneticsStatistical methods Potential theory (Mathematics) Probabilities Random fields Random matrices Random walks (Mathematics) Statistical physics Statistics Stochastic partial differential equations Stochastic processes